d2 y dy +5 = 10x(t) 2 dt dt

x(t) =

Ky(t) + r(t)

R(s) Y (s) R(s)

=

K s2 +5s+10K

Y (s) R(s)

=

10 s2 +5s+10+K

Y (s) R(s)

=

10 s2 +5s+10K

Y (s) R(s)

=

10K s2 +5s+10K

Y (s) R(s)

=

K s2 +(5+K)s+10K

2

d2 u(t) du(t) + 14 + 20u(t) dt2 dt

=

d2 y(t) dy(t) +4 + 3y(t) 2 dt dt

u(t)

Y( s)(s2 +5s) = 10X(s) X(s) =

KY (s) + R(s) 20s2 +14s+2 s2 +4s+3 s2 +4s+3 s2 +14s+20 2

Y (s)(s + 5s) = 10( KY (s) + R( s))

2s2 +14s+20 s2 +4s+3 3s2 +4s+1 2s2 +14s+20

Y (s)(s2 + 5s + 10K) = 10R(s)

Y (s) 10 = 2 R(s) s + 5s + 10K

20s2 +14s+2 3s2 +4s+1

y(t)

2s2 U + 14sU + 20U = s2 Y + 4sY + 3Y

P (s) R

Y

(2s2 + 14s + 20)U = (s2 + 4s + 3)Y Y 2s2 + 14s + 20 = U s2 + 4s + 3

P (s) =

G(s) 1 + G(s)

G(s) = f racKs(s + 10)

P (s) =

(1

K s(s+10) K + s(s+10) )

P (s) =

s2

=

K s(s + 10) + K

K Y (s) = + 10s + K R(s)

y1 = lim sY (s) s

0

R(s) = 1/s

Y (s) = P (s)R(s) =

(s2

K 1 . + 10s + K) s

y(t) 1 K 1/K 10 1/10

y1 = lim s

y1 =

0

(s2

sK 1 . + 10s + K) s

K K = =1 (0 + 10.0 + K) K

Apostila controle aeronautica